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22edo/Unque's compositional approach: Difference between revisions

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Added analyses for several scales.
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| [[Wizard, Jubilic]]
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The minor third at 6\22 is contentious in its interpretation; it is quite sharp as a representation of 6/5, though not sharp enough to constitute a neutral third. Its fifth complement, the major third at 7\22, is a much clearer 5/4, the two being practically indistinguishable to the untrained ear.
The minor third at 6\22 is contentious in its interpretation; it is quite sharp as a representation of 6/5, though not sharp enough to constitute a neutral third. Its fifth complement, the major third at 7\22, is a much clearer 5/4, the two being practically indistinguishable to the untrained ear.
{{Todo|todo:=expand|inline=1}}


== Scales ==
== Scales ==
=== 5L 2s ===
=== 5L 2s ===
The [[5L 2s]] scale is one of two types of Diatonic scales represented in 22edo, and represents 2.3.7 subgroup shade of Diatonic popularized by the Greek mathematician Archytas.
The [[5L 2s]] scale is one of two types of Diatonic scales represented in 22edo, and represents the shade of Diatonic popularized by the Greek mathematician Archytas, which uses the 2.3.7 subgroup of Just Intonation.  It is generated by the Circle of Fifths just as in common practice tunings, though the perfect fifth of 22edo is significantly sharper than any tuning attested in common practice, which makes the scale and its chords behave somewhat differently from standard Diatonic functionality.  Notably, suspended chords feel less tense and more restful, while typical tertian triads tend to sound tenser and more energetic; this is the opposite of how these chords behave in Meantone tunings, and as such Western music translated into 22edo's Diatonic may sound strange if it is not adjusted to account for its unique properties.
{| class="wikitable"
|+Modes of 5L 2s
!UDP
!Step Pattern
!Notation
!Name
|-
|<nowiki>6|0</nowiki>
|LLLsLLs
|C - D - E - F# - G - A - B - C
|Lydian
|-
|<nowiki>5|1</nowiki>
|LLsLLLs
|C - D - E - F - G - A - B - C
|Ionian
|-
|<nowiki>4|2</nowiki>
|LLsLLsL
|C - D - E - F - G - A - Bb - C
|Mixolydian
|-
|<nowiki>3|3</nowiki>
|LsLLLsL
|C - D - Eb - F - G - A - Bb - C
|Dorian
|-
|<nowiki>2|4</nowiki>
|LsLLsLL
|C - D - Eb - F - G - Ab - Bb - C
|Aeolian
|-
|<nowiki>1|5</nowiki>
|sLLLsLL
|C - Db - Eb - F - G - Ab - Bb - C
|Phrygian
|-
|<nowiki>0|6</nowiki>
|sLLsLLL
|C - Db - Eb - F - Gb - Ab - Bb - C
|Locrian
|}
 
=== 5L 7s ===
The [[5L 7s]] scale is an extension of 5L 2s created by continuing the generator sequence.  It has twelve unique rotations, which can be categorized as Grave and Acute forms of the seven diatonic modes.
{| class="wikitable"
|+Modes of 5L 7s
!UDP
!Step Pattern
!Notation
!Name
!Notes
|-
|<nowiki>11|0</nowiki>
|LsLsLssLsLss
|
|Grave Lydian
|Like the seven-note Lydian, lacks a Perfect Fourth over the root.
|-
|<nowiki>10|1</nowiki>
|LsLssLsLsLss
|
|Grave Ionian
|
|-
|<nowiki>9|2</nowiki>
|LsLssLsLssLs
|
|Grave Mixolydian
|
|-
|<nowiki>8|3</nowiki>
|LssLsLsLssLs
|
|Grave Dorian
|
|-
|<nowiki>7|4</nowiki>
|LssLsLssLsLs
|
|Grave Aeolian
|
|-
|<nowiki>6|5</nowiki>
|sLsLsLssLsLs
|
|Grave Phrygian
|Also accounts for Acute Lydian
|-
|<nowiki>5|6</nowiki>
|sLsLssLsLsLs
|
|Acute Ionian
|Also accounts for Grave Locrian
|-
|<nowiki>4|7</nowiki>
|sLsLssLsLssL
|
|Acute Mixolydian
|
|-
|<nowiki>3|8</nowiki>
|sLssLsLsLssL
|
|Acute Dorian
|
|-
|<nowiki>2|9</nowiki>
|sLssLsLssLsL
|
|Acute Aeolian
|
|-
|<nowiki>1|10</nowiki>
|ssLsLsLssLsL
|
|Acute Phrygian
|
|-
|<nowiki>0|11</nowiki>
|ssLsLssLsLsL
|
|Acute Locrian
|Like the seven-note Locrian, lacks a Perfect Fifth over the root.
|}
 
=== 3L 2M 2s ===
The [[Nicetone|3L 2M 2s]] scale is the other type of Diatonic scale represented in 22edo; this one represents the 5-limit shade of Diatonic popularized by musicians and theorists such as Ptolemy and Zarlino.  It is generated by alternating intervals 6\22 and 7\22, and as such yields two different forms ("left-hand" and "right-hand") based on which generator is comes first and which comes second.
 
The 5-limit harmony of this scale is much more reminiscent of the familiar harmony used in common-practice music, so popular music translated into this scale will be much more faithful to the harmony of the original piece than it would be using 5L 2s.
{| class="wikitable"
|+Modes of Right-hand 3L 2M 2s
!UDP
!Step pattern
!Notation
!Name
!Notes
|-
|<nowiki>6|0</nowiki>
|LMLsLMs
|C - D - Ev - F#v - G - A - Bv - C
|Lydian
|Tritone is precisely the semioctave
|-
|<nowiki>5|1</nowiki>
|LsLMsLM
|C - D - Eb^ - F^ - G - Ab^ - Bb^ - C
|Aeolian
|Contains the Wolf fourth
|-
|<nowiki>4|2</nowiki>
|LMsLMLs
|C - D - Ev - F - G - Av - Bv - C
|Ionian
|
|-
|<nowiki>3|3</nowiki>
|sLMLsLM
|C - Db^ - Eb^ - F - G - Ab^ - Bb^ - C
|Phrygian
|
|-
|<nowiki>2|4</nowiki>
|MLsLMsL
|C - Dv - Ev - F - G - Av - Bb - C
|Mixolydian
|
|-
|<nowiki>1|5</nowiki>
|sLMsLML
|C - Db^ - Eb^ - F - Gb^ - Ab^ - Bb - C
|Locrian
|Tritone is precisely the semioctave
|-
|<nowiki>0|6</nowiki>
|MsLMLsL
|C - Dv - Eb - F - Gv - Av - Bb - C
|Dorian
|Contains the Wolf fifth
|}
{| class="wikitable"
|+Modes of Left-hand 3L 2M 2s
!UDP
!Step pattern
!Notation
!Name
!Notes
|-
|<nowiki>6|0</nowiki>
|LsLMLsM
|C - D - Eb^ - F^ - G - A - Bb^ - C
|Dorian
|Contains the Wolf fourth
|-
|<nowiki>5|1</nowiki>
|LMLsMLs
|C - D - Ev - F#v - G - Av - Bv - C
|Lydian
|Tritone is precisely the semioctave
|-
|<nowiki>4|2</nowiki>
|LsMLsLM
|C - D - Eb^ - F - G - Ab^ - Bb^ - C
|Aeolian
|
|-
|<nowiki>3|3</nowiki>
|MLsLMLs
|C - Dv - Ev - F - G - Av - Bv - C
|Ionian
|
|-
|<nowiki>2|4</nowiki>
|sLMLsML
|C - Db^ - Eb^ - F - G - Ab^ - Bb - C
|Phrygian
|
|-
|<nowiki>1|5</nowiki>
|MLsMLsL
|C - Dv - Ev - F - Gv - Av - Bb - C
|Mixolydian
|Contains the Wolf fifth
|-
|<nowiki>0|6</nowiki>
|sMLsLML
|C - Db^ - Eb - F - Gb^ - Ab^ - Bb - C
|Locrian
|Tritone is precisely the semioctave
|}
When disambiguation is needed between the modes of 5L 2s and 3L 2M 2s, the former can be described as e.g. "Superpyth Ionian" or "Superpyth Aeolian," and the latter as e.g. "Nice Ionian" or "Nice Aeolian."
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